Nonlinear dynamic characteristics of mutually coupled heat-driven thermoacoustic oscillators: Dissipative and time-delay coupling effects

Complex nonlinear dynamic phenomena, such as synchronization and amplitude death, are commonly observed in mutually coupled heat-driven thermoacoustic oscillators. A comprehensive analysis of these nonlinear effects is crucial for optimizing the structural design and enhancing the performance of thermoacoustic oscillators. In this study, computational fluid dynamics (CFD) methods are employed to investigate the nonlinear dynamics of mutually coupled thermoacoustic oscillators, interacting via two distinct coupling methods: dissipative coupling and time-delay coupling. The influence of structural parameters, including resonator length, needle valve diameter, and the length and diameter of the connecting pipe, on the coupling effects is examined. CFD results reveal that synchronization, asynchronization, and amplitude death occur under dissipative coupling, while synchronization and asynchronization are observed in time-delay coupling. Under synchronous, asynchronous, and amplitude-death conditions, the oscillators exhibit periodic oscillations at a single frequency, quasi-periodic oscillations with two frequencies, and quenching of self-excited oscillations, respectively. In dissipative coupling, a larger needle valve diameter and a smaller resonator length difference are more likely to induce synchronization. In contrast, in time-delay coupling, a shorter connecting pipe length and a larger connecting pipe diameter facilitate synchronization. This study provides valuable insights into the impact of coupling methods on the performance of mutually coupled thermoacoustic oscillators. It deepens the understanding of synchronization and amplitude-death phenomena, and it offers novel approaches for exploring other nonlinear dynamic behaviors in thermoacoustic oscillators.